... Example: . of subspace a is ) }111 1(),1010(),0101(),0000{( 4 V n V n V ) }111 1() ,110 1() ,110 0(),1 011( ),1010(),1001(),1000( ), 0111 (),0101(),0100(),0 011( ),0010(),0001(),0000{( 4 =V Lecture 9 14 Some definitions… ... addition and multiplication forms a field. Binary field is also called Galois field, GF(2). 011 101 110 000 =⊕ =⊕ =⊕ =⊕ 111 001 010 000 =⋅ =⋅ =⋅ =⋅ Addition Multiplication Lecture 9 11 Some ... error detection and correction codes Lecture 9 7 Why using error correction coding? Error performance vs. bandwidth Power vs. bandwidth Data rate vs. bandwidth Capacity vs. bandwidth (dB)...